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A magnetic order can be completely suppressed at zero temperature($T$), bydoping carriers or applying pressure, at a quantum critical point(QCP), aroundwhich physical properties change drastically. However, the situation is unclearfor an electronic nematic order that breaks rotation symmetry. Here we reportnuclear magnetic resonance(NMR) studies on NaFe$_{1-x}$Co$_{x}$As wheremagnetic and nematic transitions are well separated. The NMR spectrum issensitive to inhomogeneous magnetic fields in the vortex state, which isrelated to London penetration depth $\lambda_{\rm L}$ that measures theelectron mass $m^*$. We discovered two peaks in the doping dependence of$\lambda_{\rm L}^2$($T\sim$0); one at $x_{\rm M}$=0.027 where the spin-latticerelaxation rate shows quantum critical behavior, and another at $x_{\rmc}$=0.032 around which the nematic transition temperature extrapolates to zeroand the electrical resistivity shows a $T$-linear variation. Our resultsindicate that a nematic QCP lies beneath the superconducting dome at $x_{\rmc}$ where $m^*$ is enhanced. The impact of the nematic fluctuations onsuperconductivity is discussed.

Electron Mass Enhancement near a Nematic Quantum Critical Point in NaFe$_{1-x}$Co$_{x}$As